Question 1059845

The product of two consecutive positive even numbers is 288. By forming and solving an equation, find the larger of the two numbers
<pre>Let the larger number be L
Then the smaller is: L - 2
We then get: L(L - 2) = 288________{{{L^2 - 2L - 288 = 0}}}
Since the difference in the 2 numbers is 2, then find the square root of their product, or the square root of 288: {{{sqrt(288)}}} = 16.97.
This means that one of the number is 16. Divide 288 by 16 and you get 18. The 2 numbers are 16 and 18. 
Now, {{{L^2 - 2L - 288 = 0}}} becomes: (L - 18)(L + 16) = 0 
Thus, the larger number can be 18 or - 16, but since you need the LARGER POSITIVE EVEN number, you have it. Done!!